Abstarct: In this study, a class of quantile-baxsed risk measures that generalize the value of VaR risk exposure as well as the expected loss is introduced by considering both the frequency and the severity of losses. Under VaR a single confidence level is assigned regardless of the size of potential losses. We allow for a range of confidence levels that depend on the loss magnitude. The main topic of research is the application of a benchmark loss distribution (BLD) in insurance, i.e. a function that lixnks a maximum probable probability of event to any potential loss. The corresponding risk measure, called Loss VaR (LVaR), determines the minimal capital injection that is required to align the loss distribution of a risky position to the target BLD. By design, one has full flexibility in the choice of the BLD profile and, therefore, in the range of relevant quantiles. Special attention is given to piecewise constant functions and to tail distributions of benchmark random losses. Furthermore, in this research the main theoretical properties of LVaR with a focus on their comparison with VaR and ES and discuss applications to capital adequacy, portfolio risk management, and catastrophic risk. Also, for the validation of the research, the actual data of claims paid and premiums received in the field of supplementary insurance activity of the insurance company have been used. The probability and cumulative distribution of claims paid to insurers as well as the probability and cumulative distribution of profits and losses of the insurance company from each insurer is determined by using EasyFit software and R software. Finally, the size of risks in the field of supplementary health insurance activity has been estimated and calculated by VaR, ES, LVaR and RVaR risk measures.